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(1) Why do you bother grepping for 00? Every line in your sample file already begins with 00, and, even if it didn’t, you’re just arbitrarily adding complexity to the question. (2) Luckily your question was fairly easy to understand, and your example input files helped (thank you for including them). But it’s customary, when asking a question like this, to include the corresponding expected output.
– G-ManApr 22 at 21:02

Assuming the grep -a 00 is extraneous, the following should work:
grep -vf omit.txt Filetogrepfrom.txt

WARNING: Unless you're sure that the Filetogrepfrom.txt will never contain, for example, '0011', which the omit.txt would filter out with '001', you really ought to bound your "omit.txt" using something more like -- ex: omit.txt:
^001$
^006$
^008$
^0016$

You would use -x to do matching across complete lines, or -w to do word matching. Either of these would get around the issue of matching substrings in this case. (And you would use -F to do string comparisons).
– Kusalananda♦Apr 18 at 19:22